ESP32 CODE implementation of FOC control method for BLDC MOTOR

Work in progress for the esp32 code of the FOC algorithm for actual control of a BLDC motor.

ESP-32 Pin-Out

Mathematical model for the BLDC motor

$$ \frac{d}{dt} \left(\begin{array}{c} I_a\\ I_b \\ I_c \\ \omega_r \\ \theta_e \end{array}\right) = \left(\begin{array}{ccccc} -\frac{R}{L-M} & 0 & 0 & -\frac{P_p\phi_mF_a(\theta_e)}{L-M} & 0\\ 0 & -\frac{R}{L-M} & 0 & -\frac{P_p\phi_mF_b(\theta_e)}{L-M} & 0\\ 0 & 0 & -\frac{R}{L-M} & -\frac{P_p\phi_mF_c(\theta_e)}{L-M} & 0\\ 0 & 0 & -\frac{R}{L-M} & -\frac{P_p\phi_mF_c(\theta_e)}{L-M} & 0\\ \frac{P_p\phi_mF_A(\theta_e)}{J} & \frac{P_p\phi_mF_B(\theta_e)}{J} & \frac{P_p\phi_mF_C(\theta_e)}{J} & -\frac{B}{J} & 0 \\ 0 & 0 & 0 & P_p & 0 \end{array}\right) \left(\begin{array}{c} I_a \\ I_b \\ I_c \\ \omega_r \\ \theta_e \end{array}\right) + \left(\begin{array}{cccc} \frac{1}{L-M} & 0 & 0 & 0\\ 0 & \frac{1}{L-M} & 0 & 0\\ 0 & 0 & \frac{1}{L-M} & 0\\ 0 & 0 & 0 & -\frac{1}{J} \\ 0 & 0 & 0 & 0 \end{array}\right) \left(\begin{array}{c} V_an \\ V_bn \\ V_cn \\ T_c \end{array}\right) $$

FOC mathematical operations

Clarke transform

$$ \left(\begin{array}{c} V_0 \\ V_\alpha \\ V_\beta \end{array}\right) = \sqrt{\frac{2}{3}} \left(\begin{array}{ccc} \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} & \sqrt{\frac{1}{2}} \\ 1 & -\frac{1}{2} & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \end{array}\right) \left(\begin{array}{c} V_A \\ V_B \\ V_C \end{array}\right) $$

Clarke Inverse Transform

$$ \left(\begin{array}{c} V_A \\ V_B \\ V_C \end{array}\right) = \left(\begin{array}{ccc} \frac{\sqrt{2}}{2} & 1 & 0\\ \frac{\sqrt{2}}{2} & -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \frac{\sqrt{2}}{2} & -\frac{1}{2} & -\frac{\sqrt{3}}{2} \end{array}\right) \left(\begin{array}{c} V_0 \\ V_\alpha \\ V_\beta \end{array}\right) $$

Park Transform

$$ \left(\begin{array}{c} V_d \\ V_q \end{array}\right) = \left(\begin{array}{cc} \cos(\theta) & \sin(\theta) \\ -\sin(\theta) & \cos(\theta) \end{array}\right) \left(\begin{array}{c} V_\alpha \\ V_\beta \end{array}\right) $$

Inverse Park Transform

$$ \left(\begin{array}{c} V_\alpha \\ V_\beta \end{array}\right) = \left(\begin{array}{cc} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{array}\right) \left(\begin{array}{c} V_d \\ V_q \end{array}\right) $$

V/F Control tactic

For the first run tests, the V/F OpenLoop method was choose.

V/F Control is a open loop method that consist of aplying a gain value for the Voltage of the motor pins.

$$ G_f = \frac{V_{max}}{\omega_{max}} \\ V_{max} = G_f \omega_{max} $$

Code example:

Volts = ref*Gf*gain_adc;
comp_value = Volts*BLDC_MCPWM_PERIOD/Tmax;

//here is where de duty cycle is defined
duty_A = comp_value*FEM_sin(theta);
duty_B = comp_value*FEM_sin(theta + pi/3.0);
duty_C = comp_value*FEM_sin(theta - pi/3.0);

by changing the value of the $\omega$ we can adjust the Voltage value so the motor can run.

Another necessary step is muntiplying the $\omega_{ref}$ that comes form the reference to the Gain of the V/F method by all the 3 phases FEM curve.

Motor specs

For this work i will be using a A2212/13T brushless motor.

• Resistance 0.090$\Omega$
• Poles 14
• Inductance 0.1mH

Calculations

$ K_v = \frac{\omega_{rpm}}{V_P0.95} $

$K_v$ - is the voltage constante of a motor, rought means how many rotations the motor will go for every Volt.

$ K_p = \frac{60}{2 \pi K_v} $ if Kv in rpm

for Kv in rad it simply is the inverse of Kp

$ K_p = \frac{1}{K_v} $